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Turbulent flow in a square duct with strong curvature

Published online by Cambridge University Press:  20 April 2006

J. A. C. Humphrey ,
J. H. Whitelaw  and
G. Yee
J. A. C. Humphrey
Affiliation:
Department of Mechanical Engineering, University of California, Berkeley, California
J. H. Whitelaw
Affiliation:
Department of Mechanical Engineering, Fluids Section, Imperial College, London
G. Yee
Affiliation:
Science Applications Incorporated, San Leandro, California
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Abstract

The steady, incompressible, isothermal, developing flow in a square-section curved duct with smooth walls has been investigated. The 40 × 40 mm duct had a radius ratio of 2·3 with long upstream and downstream straight ducts attached. Measurements of the longitudinal and radial components of mean velocity, and corresponding components of the Reynolds-stress tensor, were obtained with a laser-Doppler anemometer at a Reynolds number of 4 × 104 and in various cross-stream planes. The secondary mean velocities, driven mainly by the pressure field, attain values up to 28% of the bulk velocity and are largely responsible for the convection of Reynolds stresses in the cross-stream plane. Production of turbulent kinetic energy predominates close to the outer-radius wall and regions with negative contributions to the production exist. Thus, at a bend angle of 90° and near the inner-radius wall, $\overline{u_{\theta}u_r}\partial U_{\theta}/\partial r$ is positive and represents a negative contribution to the generation of turbulent kinetic energy.

In spite of the complex mean flow and Reynolds stress distributions, the cross-stream flow is controlled mainly by the centrifugal force, radial pressure gradient imbalance. As a consequence, calculated mean velocity results obtained from the solution of elliptic differential equations in finite difference form and incorporating a two-equation turbulence model are not strongly dependent on the model; numerical errors are of greater importance.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 103 , February 1981 , pp. 443 - 463
Copyright
© 1981 Cambridge University Press

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